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In this talk, we study the Gromov-Hausdorff convergence of Ricci-flat metrics under degenerations of Calabi-Yau manifolds. More precisely, for a family of polarized Calabi-Yau manifolds degenerating to a singular Calabi-Yau variety, we prove that the Gromov-Hausdorff limit of Ricci-flat kahler metrics on them is unique.